Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
8001	18855^2402+2402^18855	63741	Hans Havermann	03/2017
8002	(142*10^63734-7)/9	63736	Robert Price	02/2017
8003	2^211699-111	63728	Lelio R Paula	08/2011
8004	11^61192-5550	63725	Enzo Doria	01/2013
8005	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
8006	6^81872-13	63709	Lelio R Paula	04/2013
8007	3^133522+98	63707	Lelio R Paula	05/2013
8009	2^211607-61	63701	Lelio R Paula	08/2011
8008	5^91135+8	63701	Lelio R Paula	04/2013
8010	11^61157-270	63689	Enzo Doria	07/2012
8012	10^63685+1145141919	63686	Marisa Kirisame	03/2015
8011	10^63685+103837	63686	Patrick De Geest	03/2016
8013	10^63685-130797	63685	Patrick De Geest	03/2016
8014	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
8015	2^211543+45	63681	Lelio R Paula	08/2011
8016	2^211534+43	63679	Lelio R Paula	08/2011
8017	11^61140-60	63671	Enzo Doria	07/2012
8018	2^211491-112321	63666	Enzo Doria	06/2014
8019	19085^2164+2164^19085	63654	Hans Havermann	03/2017
8020	(2^211430-5)/859	63644	Lelio R Paula	04/2012
8021	2^211401-91	63639	Lelio R Paula	08/2011
8022	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
8023	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
8024	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
8025	2^211333+15015	63618	Lelio R Paula	01/2013
8026	33^41889-32	63610	Norbert Schneider	03/2014
8027	13^57093+18	63599	Lelio R Paula	05/2013
8028	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
8029	(107*10^63576-17)/9	63578	Robert Price	02/2017
8030	23^46687-1020	63575	Enzo Doria	08/2012
8031	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
8032	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
8033	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
8035	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
8034	2*3^133227+5	63566	Lelio R Paula	04/2014
8036	2^211155+113	63564	Lelio R Paula	08/2011
8037	2^211134+345	63558	Lelio R Paula	09/2011
8038	2^211121+16385	63554	Lelio R Paula	09/2011
8039	16996^5483+5483^16996	63549	Hans Havermann	02/2017
8040	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
8041	3*10^63522+13	63523	Robert Price	08/2017
8042	15852^10157+10157^15852	63516	Hans Havermann	02/2017
8043	2^210948-15873	63502	Enzo Doria	04/2013
8044	7^75136+6	63498	Lelio R Paula	04/2013
8045	2^210928+12915	63496	Lelio R Paula	02/2013
8046	7*10^63493+39	63494	Robert Price	07/2016
8047	2^210909+135	63490	Lelio R Paula	08/2011
8048	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
8049	8*7^75098-3	63467	Lelio R Paula	09/2014
8050	17683^3882+3882^17683	63466	Hans Havermann	03/2017
8052	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
8051	2^210820-16905	63464	Enzo Doria	05/2013
8054	5^90795-36	63463	Lelio R Paula	04/2013
8053	84731!6-48	63463	Robert Price	08/2018
8055	2^210816-13197	63462	Enzo Doria	10/2012
8056	2^210750+133	63443	Lelio R Paula	08/2011
8057	291^25742+25742^291	63426	Norbert Schneider	09/2014
8058	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
8059	6^81480-139	63404	Lelio R Paula	04/2013
8060	2^210576-173	63390	Lelio R Paula	08/2011
8061	18^50497+55	63388	Lelio R Paula	05/2013
8062	2^210545+11	63381	Lelio R Paula	08/2011
8063	2^210543+63	63380	Lelio R Paula	08/2011
8064	155^28929-154	63365	Norbert Schneider	12/2018
8065	83^33016+82	63361	Norbert Schneider	04/2015
8066	2^210464+98765331	63356	Jason Earls	12/2008
8067	7*10^63351+9	63352	Dmitry Domanov	11/2010
8068	p(13534)#/2+512	63348	Robert Price	05/2017
8069	1741^19546+19546^1741	63345	Serge Batalov	05/2014
8070	10^63336+19819	63337	Patrick De Geest	12/2013
8071	10^63336-122883	63336	Patrick De Geest	12/2013
8072	(19^49523-2^49523)/17	63327	Robert Price	09/2013
8073	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
8074	31191!2+256	63316	Robert Price	01/2015
8075	16458^7031+7031^16458	63315	Hans Havermann	01/2017
8076	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
8077	156^28864+155	63303	Norbert Schneider	12/2018
8078	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
8079	2^210217+1299	63282	Lelio R Paula	09/2011
8080	(2^210221-3)/269	63281	Lelio R Paula	04/2012
8081	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
8082	96^31913-95	63261	Norbert Schneider	04/2016
8083	3^132572+280	63253	Lelio R Paula	04/2013
8084	3^132570-2^(132570-1)	63252	Robert Price	01/2016
8085	11^60734-4920	63248	Enzo Doria	01/2013
8087	2^210061+21	63235	Donovan Johnson	06/2006
8086	18^50375+95	63235	Lelio R Paula	05/2013
8088	85^32773-2	63233	Lelio R Paula	08/2013
8089	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
8090	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
8091	3*2^210022+5	63224	Lelio R Paula	04/2014
8092	15^53756+32	63222	Lelio R Paula	05/2013
8094	17^51380+22	63221	Lelio R Paula	05/2013
8093	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
8095	43^38700+42	63216	Norbert Schneider	06/2014
8096	5^90431-96	63209	Lelio R Paula	04/2013
8097	(172*10^63202-1)/9	63204	Serge Batalov	12/2014
8098	(43*10^63200+83)/9	63201	Robert Price	08/2017
8099	2^209914-16005	63191	Enzo Doria	04/2013
8100	3*6^81190-5	63179	Lelio R Paula	09/2014
8101	2^209820+4257	63163	Lelio R Paula	10/2011
8102	99^31648+2	63158	Lelio R Paula	05/2013
8103	16976^5253+5253^16976	63158	Hans Havermann	01/2017
8104	2^209790+67	63154	Lelio R Paula	08/2011
8105	145878#-p(145878)	63152	Henri Lifchitz	12/2018
8106	2^209759+90195	63144	Lelio R Paula	02/2013
8107	145823#+211507	63142	Arkadiusz Wesolowski	03/2013
8109	2^209707+513	63129	Lelio R Paula	10/2011
8108	(3^132314-8)/17	63129	Lelio R Paula	04/2012
8110	(2*10^63117+7)/9	63117	Erik Branger	03/2011
8111	9*2^209654-7	63114	Lelio R Paula	04/2014
8112	84304!6-9	63112	Robert Price	08/2018
8113	11^60598-14	63107	Lelio R Paula	05/2013
8114	15103^15078+15078^15103	63106	Hans Havermann	01/2017
8115	15346^12941+12941^15346	63103	Hans Havermann	01/2017
8116	3^132253+76	63101	Lelio R Paula	04/2013
8117	(56*10^63100+403)/9	63101	Robert Price	10/2017
8118	17549^3936+3936^17549	63090	Hans Havermann	01/2017
8119	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
8120	(331^25033-1)/330	63077	Eric Chen	09/2017
8121	20^48480+31	63074	Lelio R Paula	06/2013
8122	(26*10^63073-23)/3	63074	Robert Price	08/2016
8123	2^209499+76253	63066	Enzo Doria	04/2016
8124	11^60546-11340	63053	Enzo Doria	12/2012
8125	2^209426+57889	63044	Yves Minet	02/2010
8126	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
8127	5^90189+54	63040	Lelio R Paula	04/2013
8128	(22*10^63034-73)/3	63035	Robert Price	09/2017
8129	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
8130	V(301486)	63007	Henri Lifchitz	05/2003
8131	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
8132	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
8133	6^80946-5^(80946-1)	62989	Robert Price	05/2016
8134	467^23596+23596^467	62986	Norbert Schneider	08/2016
8135	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
8136	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
8137	1456^19909+19909^1456	62976	Serge Batalov	05/2014
8138	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
8139	35^40772-1466	62955	Enzo Doria	03/2013
8140	5^90064-13706	62953	Enzo Doria	02/2013
8141	(22*10^62926+257)/9	62927	Robert Price	11/2017
8142	(13*10^62914+401)/9	62915	Robert Price	10/2017
8143	2^208993+107	62914	Lelio R Paula	08/2011
8144	2^208993+77	62914	Lelio R Paula	08/2011
8145	189^27636-2	62913	Lelio R Paula	10/2017
8146	(2^208948-7)/261	62898	Lelio R Paula	03/2012
8147	(151*10^62879-1)/3	62881	Robert Price	04/2017
8148	15^53464-82	62879	Lelio R Paula	05/2013
8149	2^208843-112921	62869	Enzo Doria	06/2014
8150	2^208779+81	62849	Henri Lifchitz	01/2007
8151	159^28548+158	62846	Norbert Schneider	12/2018
8152	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
8153	(73*10^62824+17)/9	62825	Robert Price	10/2015
8154	3^131670-82	62823	Lelio R Paula	04/2013
8155	19^49128-90	62823	Lelio R Paula	05/2013
8156	11^60314-4410	62811	Enzo Doria	01/2013
8157	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
8158	2^208594+93	62794	Donovan Johnson	06/2008
8159	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
8160	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
8162	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
8161	10^62750+57	62751	Robert Price	01/2011
8163	10^62750-267429	62750	Patrick De Geest	01/2013
8164	2^208427-69	62743	Lelio R Paula	08/2011
8165	2^208421-111775	62741	Enzo Doria	05/2014
8166	2^208404-112079	62736	Enzo Doria	06/2014
8167	2^208343-2221	62718	Yves Minet	08/2013
8168	2^208335+513	62716	Lelio R Paula	10/2011
8169	(2^208328+47)/3	62713	Lelio R Paula	03/2012
8170	11^60220-2040	62713	Enzo Doria	12/2012
8171	2^208292+81	62703	Henri Lifchitz	10/2005
8172	15013^15012-15012	62698	Henri Lifchitz	10/2014
8173	2^208271-112747	62696	Enzo Doria	06/2014
8174	11^60202-4380	62694	Enzo Doria	01/2013
8175	(3^131403-4)/157	62693	Lelio R Paula	04/2012
8176	2^208127-126667	62653	Paul Bourdelais	01/2012
8177	71^33843+2	62653	Lelio R Paula	05/2013
8178	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
8179	2^208019+119	62620	Lelio R Paula	08/2011
8180	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
8181	11^60126-11370	62615	Enzo Doria	12/2012
8182	2^207976-2489	62608	Yves Minet	07/2014
8183	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
8184	4*21^47335+205	62588	Curtis Bright	05/2015
8185	15^53210+8	62580	Lelio R Paula	05/2013
8186	2^207865+29	62574	Henri Lifchitz	08/2005
8187	15^53199-38	62567	Lelio R Paula	05/2013
8188	(F(24947)^13-F(24946)^13)/F(24945)	62560	Wayne Halsdorf	03/2012
8189	2^207782+58905	62549	Lelio R Paula	10/2011
8190	(2^207748-3)/8437	62535	Lelio R Paula	03/2012
8191	(2^207711+5)/13	62527	Lelio R Paula	03/2012
8192	(268*10^62523-1)/3	62525	Robert Price	10/2017
8193	10^62523+63	62524	Robert Price	01/2011
8194	10^62523-292373	62523	Patrick De Geest	01/2013
8196	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
8195	(lucasV(1,2,415410)+2)/(17*653)	62522	Mike Oakes	02/2017
8197	2^207626-112157	62502	Enzo Doria	06/2014
8198	3^130987+52	62497	Lelio R Paula	04/2013
8199	8*6^80299-7	62486	Lelio R Paula	09/2014
8200	11^59997-2670	62481	Enzo Doria	12/2012
8201	93^31740+2	62480	Lelio R Paula	05/2013
8202	(10^62451+119)/3	62451	Serge Batalov	12/2014
8203	(2^207443+47)/7645	62443	Lelio R Paula	03/2012
8204	2^207364+115	62423	Lelio R Paula	08/2011
8205	3^130815-46	62415	Lelio R Paula	04/2013
8206	(F(182)^1657-F(181)^1657)/F(180)	62409	Wayne Halsdorf	03/2012
8207	20^47968-9483	62408	Enzo Doria	03/2013
8208	(10^62402+101)/3	62402	Robert Price	04/2016
8209	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
8210	(79*10^62387-61)/9	62388	Robert Price	10/2015
8211	5^89244+3*2^89244	62379	Mike Oakes	02/2010
8212	6^80160-13	62377	Lelio R Paula	04/2013
8213	(7*10^62362+53)/3	62363	Robert Price	10/2017
8214	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
8215	(17*10^62328-11)/3	62329	Robert Price	07/2015
8216	2^207023+11715	62321	Lelio R Paula	09/2011
8217	(265*10^62298+11)/3	62300	Robert Price	03/2017
8218	2^206947-69	62298	Lelio R Paula	08/2011
8219	2^206938+29835	62295	Lelio R Paula	02/2013
8220	2^206911-726877	62287	Paul Bourdelais	03/2013
8221	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
8222	2^206892-112817	62281	Enzo Doria	06/2014
8223	(7*10^62278+113)/3	62279	Robert Price	10/2017
8224	3^130523+46	62276	Lelio R Paula	04/2013
8225	2^206872-113453	62275	Enzo Doria	07/2014
8226	2^206840-93	62266	Lelio R Paula	08/2011
8227	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
8228	96^31406+95	62256	Norbert Schneider	03/2016
8229	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
8230	2^206765-941683	62243	Paul Bourdelais	11/2012
8231	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
8232	2^206755-1579	62240	Yves Minet	03/2013
8233	11^59764-5820	62238	Enzo Doria	01/2013
8234	5*10^62233+3	62234	Dmitry Domanov	11/2010
8235	8*3^130421+7	62228	Lelio R Paula	04/2014
8236	19^48661+10	62226	Lelio R Paula	05/2013
8237	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
8238	2^206705-112635	62225	Enzo Doria	06/2014
8239	3^130403+8680	62219	Lelio R Paula	04/2013
8240	11^59740-7110	62213	Enzo Doria	01/2013
8242	2^206596-167	62192	Lelio R Paula	08/2011
8241	2^206597+18915	62192	Lelio R Paula	02/2013
8243	6^79918+137	62189	Lelio R Paula	04/2013
8244	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
8245	2^206574+613	62185	Jason Earls	04/2008
8246	3^130328+80	62183	Lelio R Paula	04/2013
8247	(lucasV(1,2,413270)-2)/(11^2234431871200337571687961)	62181	Mike Oakes	02/2017
8248	2^206550+76819	62178	Enzo Doria	05/2016
8249	11^59703-24	62175	Lelio R Paula	05/2013
8250	2^206524+75781	62170	Enzo Doria	04/2016

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Probable Primes Top 10000

(252675 PRPs in the top)